Field of Rational Numbers
From ProofWiki
Theorem
The set of rational numbers $\Q$ forms a totally ordered field under addition and multiplication: $\left({\Q, +, \times, \le}\right)$.
Proof
This is demonstrated in the formal definition of rational numbers.
$\blacksquare$
Sources
- Iain T. Adamson: Introduction to Field Theory (1964)... (previous)... (next): $\S 1.1$: Example $2$
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 23$
- C.R.J. Clapham: Introduction to Abstract Algebra (1969)... (previous)... (next): $\S 4.15$: Example $14$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 19$
